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Plot multivariable function, find critical points

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PJ
PJ 2018-1-18
评论： Star Strider 2018-1-19
i need to plot a multivariable (x1,x2) function f_a in matlab, and find its critical points. I plotted it, but in order to find the critical points, i need to set the partial derivatives to zero then solve. when i try setting the partial derivatives to zero using diff(f_a,x1),it gives me an error.
[x1,x2] = meshgrid(-5:.2:5);
f_a = x1.^2 + x2.^2 +2.*x1.*x2;
figure(1)
surf(x1,x2,f_a)
fa1=diff(f_a,x1)

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Star Strider
Star Strider 2018-1-18
Use the gradient function to calculate the derivative.
Try this:
[x1,x2] = meshgrid(-5:.2:5);
f_a = x1.^2 + x2.^2 +2.*x1.*x2;
fa1 = gradient(f_a, 0.2, 0.2); % Derivative
zv = contour(x1,x2,fa1, [0; 0]); % Critical Points
figure(1)
surf(x1,x2,f_a)
hold on
plot3(zv(1,2:end), zv(2,2:end), zeros(1,size(zv,2)-1), 'r', 'LineWidth',2)
hold off
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PJ
PJ 2018-1-19
I tried it for another function and i'm not sure if it is giving me correct figures because there seems to be 3 red lines as contour lines, and I added another contour plot and found the critical points after, but the contour plot of figure 2 did not match the red lines of figure 1. I'm sure this is repetitive, but could you please take a look:
[x1,x2] = meshgrid(-5:.2:5);
f_c = x1.^4 + x2.^4 +1 -x1.^2+x2.^2;
figure(1)
surf(x1,x2,f_c)
[fc1,fc2] = gradient(f_c,0.2,0.2); %what do the 0.2s represent?
zv = contour(x1,x2,fc1, [0; 0]); %what do the 0s represent?
figure(1)
surf(x1,x2,f_c)
hold on
plot3(zv(1,2:end), zv(2,2:end), zeros(1,size(zv,2)-1), 'r', 'LineWidth',2 )
hold off
figure (2)
contour(x1,x2,f_c)
hold on
quiver(x1,x2,fc1,fc2)
hold off
syms x1 x2
fc1=diff(x1.^4 + x2.^4 +1 -x1.^2+x2.^2,x1);
fc2=diff(x1.^4 + x2.^4 +1 -x1.^2+x2.^2,x2);
[x1cr,x2cr]=solve(fc1,fc2);
critical_points=[x1cr,x2cr]
Star Strider
Star Strider 2018-1-19
‘what do the 0.2s represent?’
They are the differences between the consecutive values of the meshgrid values in each direction.
‘what do the 0s represent?’
They specify that I want the contour function to trace out and return only the contours at 0.
I cannot follow what you are doing in the code you posted.

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